Why is Composite Blur square
A "true" gaussian blur is not limited by distance - if the 'centre' point is strong enough it would have an effect on even the most distant pixels in the image (the gaussian distribution falls off towards zero as the distance increases but never actually reaches it). For efficiency, the Gaussian blur in Blender is limited by range in each of the X and Y directions - so the value falls off with distance but cuts off at the edge of the range. Since the range is determined only in the X and Y directions this forms a 'square of effect' of the blur from any pixel in your image.

This would not normally cause a problem since relatively low intensity pixels would naturally drop off to very close to zero at the edge of the range when the gaussian blur is taken into effect. However, in your case you have extremely large values for your bright points. This means that the gaussian has not dropped quite so close to zero at the edge of its range to be unnoticeable and so the edge of that 'square of effect' is noticeable.

The only solutions I can suggest are to either limit the brightest stars to lower values or to blur them in multiple stages to 'spread' their impact more evenly - eg, instead of a single Blur of 20x20 you could use one at 10x10 to soften them out followed by another at 17x17 (I picked these values 'by eye') to produce the following :



(The left-hand side is the 'single' blur (showing the square artifact edge) while the right-hand is the 'double' blur)